Could You Charge a Smartwatch by Shaking It?

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Could You Charge a Smartwatch by Shaking It?

Smartwatches are cool. They can give you smartphone-like access to data without the phone. However, as Uncle Ben said (Spider-Man's uncle):

"With great power in a smartwatch comes terrible battery life."

Ok, Uncle Ben didn't actually say that - but he would have if he had a smartwatch. Also, I will admit that the battery life on the Pebble watch (seen above) isn't so bad. But with more features in a watch, battery life can be an issue. Who wants to charge a watch every night like you have to do with your smartphone? "No one" is the correct answer. No one wants to keep charging a smartwatch.

I have an older watch that is completely mechanical (no battery). This watch is really cool because you don't wind it up. Instead, there is a weight inside that moves back and forth as you walk around and do stuff. This moving weight essentially winds the watch up for you. Could something like this work for a smartwatch?

Electromagnetic Charging
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A mechanical watch stores energy in a spring - but this isn't true for an electric watch. Those need an electric battery. One way to charge a battery is with a permanent magnet and a coil of wire. This is the basic idea in these "shake lights". You just shake the flashlight for a little bit and then the flashlight works for a while.

Here is a diagram of the basic setup for one of these flashlights.

As the magnet moves into the coil of wire (from shaking the light), there is a changing magnetic field. This changing magnetic field induces an electric current in the wire to charge the battery - actually I think the shake light uses a capacitor instead.

But how much energy could get from something like this? It wouldn't be hard to build a small model to measure output energy values, but let me just approximate instead. Really, all the energy comes from a change in kinetic energy of the magnetic. Let's say the magnet has a mass m and enters the coil with a velocity of v1 then leaves with a velocity v2. The change in energy for this one motion would be:

Of course all of this energy wouldn't actually go into charging the battery. That would only be true if the device was 100% efficient - which nothing is. However, I am just going to assume there is no energy loss. I'll explain why after the calculation.

So how would this work in a smartwatch? It would be exactly the same, just smaller. You would have a smaller magnet and a smaller coil, but the idea would be the same. How about some estimates? Really, I just need three things. I need the mass of the magnet and the starting and ending velocities during the motion.

First, for the mass estimate. The Pebble smartwatch has a mass of 39 grams (including the watch band). I think a magnet mass of over 10 grams would just be a little crazy.

Second, I need the starting and ending velocity of the magnet. This is a bit more difficult. Let me start by approximating an arm swing. Suppose that the wrist moves 1 meter in 1 second in the process of an arm swing (yes, that is a fast and large swing). During this swinging motion, the wrist speeds up for half of that time and then slows down for the other half. This means that the the wrist (and watch) start from rest, move 0.5 meters in 0.5 seconds. I can write the average velocity as:

But this is just the average speed. Really, I want the final velocity during this part of the swing. If I assume a constant acceleration, I can write the average velocity as:

Since the initial velocity was zero, the final velocity would have to be twice the average - that puts it at 2 m/s. Note that this is the velocity of the watch at the midpoint in the swing. I will use this for the velocity of the magnet as it enters the coil. What about after leaving the coil? Realistically, the exiting velocity would just be a little bit slower than the beginning velocity. However, for this estimation I will say that it is going half the initial speed afterwards.

Using this, I get an energy of 0.015 Joules per arm swing. That's great, but how much arm swinging would you need to charge a Pebble battery? This site on ifixit shows the Pebble battery as a 3.7 Volt with 130 mAh. This means that it could produce 130 mAmps at 3.7 Volts for 1 hour. In an electric circuit, power is current times voltage. With a time interval of 1 hour, I can find the energy in this battery.

Putting in the values for current, voltage and time, I get an energy of 1732 Joules.

So, how many arm swings would you need to charge the smartwatch? Since the battery stores 1732 Joules and you get 0.015 Joules per swing, I get 1.15 x 105 arm swings. Now that seems like a lot of arm swinging - but wait! You don't have to do all of those swings at once (which would be impossible). In order to make this smartwatch work, you would need to charge it over the life of the battery. Let's say the Pebble watch lasts 6 days without charging (which seems to be above the average length of time). How often would I need to swing my arm to get the number of swings needed?

Converting 6 days into seconds, I get a arm swing frequency of 0.22 swings per second. Ok, let's adjust for sleeping time. If I sleep 6 hours a night then that would increase the swing rate to 0.29 swings per second or one swing every 3.37 seconds.

That still seems pretty high. If I just think about what I am doing right now, my arm isn't swinging at all. I'm just typing. Sure, I walk around - but even then I don't make giant swings with my arm. So, will this work? I am going to say no - unless you are a marathon runner, then you are all set.

How Could You Make it Work?
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Let's look back and see why this didn't work. Consider the following:

I made lots of guesses and assumptions.

I suspected that this swinging to charge method wouldn't work. So when I estimated values, I picked values that would give me the best possible case to charge the phone (estimate high on velocities and arm swings and stuff).

If the swing still doesn't give enough energy in this case, it's not going to work with a more realistic calculation.

It's possible to build a sample wrist motion charger - it wouldn't be too difficult. However, based on this calculation it would give a lower energy production than my 0.015 Joules per swing. And this is exactly why we do back of the envelope calculations (even though we don't use envelopes).

But what could you do to increase the power production? Of course you could increase the mass of the magnet, but even doubling the mass wouldn't really be enough. What about some other charging method? What about a wireless charger? I'm going to guess this wouldn't work either - but I'll take a shot at wireless charging in a future post.